I am trying to update some of the interacts from the MAA Prep workshop so that they can be included in the UTMOST Sage cell repo. Here is an example of what I came up with:
@interact
def _(f = input_box(default=sin(x)*e^(-x)),order=slider(1,20, step_size=1), x0=("$x_0$", slider(0,4, step_size=0.25))):
p = plot(f,(x,-1,5), thickness=2)
ft = f.taylor(x, x0, order)
pt = plot(ft(x),(x,-1, 5), color='green', thickness=2)
dot = point((x0,f(x0)),pointsize=80,rgbcolor=(1,0,0))
pretty_print(html('$f(x)\;=\;%s$'%latex(f(x))))
pretty_print(html('$\hat{f}(x;%s)\;=\;%s+\mathcal{O}(x^{%s})$'%(x0,latex(ft(x)),order+1)))
show(dot + p + pt, ymin = -.5, ymax = 1)